The reaction of cyanamide, \(NH _{2} CN _{( s )}\) with oxygen was run in a bomb calorimeter and \(\Delta U\) was found to be \(-742.24\, kJ\, mol ^{-1}\). The magnitude of \(\Delta H _{298}\) for the reaction \(NH _{2} CN _{( s )}+\frac{3}{2} O _{2}( g ) \rightarrow N _{2( g )}+ O _{2}( g )+ H _{2} O _{(l)}\) is ............ \(kJ\). (Rounded off to the nearest integer) [Assume ideal gases and \(\left. R =8.314\, J\, mol ^{-1} K ^{-1}\right]\)

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason \(R\) Assertion \(A\) : Zero orbital overlap is an out of phase overlap. Reason \(R\) : It results due to different orientation/ direction of approach of orbitals. In the light of the above statements. Choose the correct answer from the options given below.

Which one of the following compounds will not be soluble in sodium bicarbonate ?

In a solvent \(50\, \%\) of an acid \(HA\) dimerizes and the rest dissociates. The van't Hoff factor of the acid is \(.....\,\times 10^{-2}\). (Round off to the nearest integer)

On combustion 0.210 g of an orgainc compound containing \(\mathrm{C}, \mathrm{H}\) and O gave \(0.127 \mathrm{~g} \mathrm{H}_2 \mathrm{O}\) and 0.307 \(\mathrm{g} \mathrm{CO}_2\). The percentages of hydrogen and oxygen in the given organic compound respectively are _______.

In the reaction of formation of sulphur trioxide by contact process \(2S{O_2} + {O_2} \rightleftharpoons 2S{O_3}\) the rate of reaction was measured as \(\frac{{d\left[ {{O_2}} \right]}}{{dt}} =  - 2.5 \times {10^{ - 4}}\,mol\,{L^{ - 1}}\,{s^{ - 1}}\) . The rate of reaction is terms of \([SO_2]\) in \(mol\,L^{- 1}\, s^{-1}\) will be:

The cell potential for \(Zn \left| Zn ^{2+}( aq ) \| Sn ^{ x +}\right| Sn\) is \(0.801\) \(V\) at \(298\,K\). The reaction quotient for the above reaction is \(10^{-2}\). The number of electrons involved in the given electrochemical cell reaction is. .... (Given \(E _{ Zn ^{2+} \mid Zn }^{0}=-0.763\,V , E _{ Sn ^{ x +} \mid Sn }^{0}=+0.008\,V\) and \(\left.\frac{2.303\,RT }{ F }=0.06\,V \right)\)

\(\)f(x)=\left| {\begin{array}{*{20}{c}} {{{\sin }^2}x}&{ - 2 + {{\cos }^2}x}&{\cos 2x} \\ {2 + {{\sin }^2}x}&{{{\cos }^2}x}&{\cos 2x} \\ {{{\sin }^2}x}&{{{\cos }^2}x}&{1 + \cos 2x} \end{array}} \right| ,x \in[0, \pi]\(\) Then the maximum value of \(f(x)\) is equal to \(.....\)

A salt with few drops of conc. HCl gives apple green colour in flame test. The group precipitate of the salt is dissolved in acetic acid and treated with \(K_2CrO_4\) to give yellow precipitate. When the sodium carbonate extract of the salt solution is heated with conc. \(HNO_3\) and ammonium molybdate, it resulted a canary yellow precipitate. The cation and anion present in the salt are respectively,

Given below are two statements :
Statement (I) : Molal depression constant \(\mathrm{K}_{\mathrm{f}}\) is given by \(\frac{M_1 R T_f}{\Delta S_{f u s}}\), where symbols have their usual meaning.
Statement (II) : \(\mathrm{K}_{\mathrm{f}}\) for benzene is less than the \(\mathrm{K}_{\mathrm{f}}\) for water.
In the light of the above statements, choose the most appropriate answer from the options given below :

The degenerate orbitals of \([Cr(H_2O)_6]^{3+}\) are

For a statistical data \(\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{10}\) of 10 values, a student obtained the mean as 5.5 and \(\sum_{i=1}^{10} x_i^2=371\). He later found that he had noted two values in the data incorrectly as 4 and 5 , instead of the correct values 6 and 8 , respectively. The variance of the corrected data is

In a survey of \(220\) students of a higher secondary school, it was found that at least \(125\) and at most \(130\) students studied Mathematics; at least \(85\) and at most \(95\) studied Physics; at least \(75\) and at most \(90\) studied Chemistry; \(30\) studied both Physics and Chemistry; \(50\) studied both Chemistry and Mathematics; \(40\) studied both Mathematics and Physics and \(10\) studied none of these subjects. Let \(\mathrm{m}\) and \(\mathrm{n}\) respectively be the least and the most number of students who studied all the three subjects. Then \(\mathrm{m}+\mathrm{n}\) is equal to ...........